Figure 3.

Combined wit h th e fac t tha t ^

q

i s a non-negativ e function , th e latte r

shows that th e integra l i n formula (1.2) is minimal whe n al l the coordinate s

of the vecto r £ are equal , an d i t i s maximal whe n on e o f the coordinate s i s

equal t o 1 and th e other s ar e equa l t o zero .

D

Figure 4 . £^-ball s

To conclude thi s sectio n le t u s give an overvie w o f known result s o n th e

extremal section s o f £™-balls.

• q — o o

max: £ = ( ^ , ^ , 0 , . . . ,0) , Ball [Bai ]

min: £ = (1,0, ...,0), Hadwige r [Ha] , Hensle y [He] , Vaale r

[V]

• 0 q 2

max: £ = (1,0,..., 0), Meyer-Pajor [MeyP ] ( 1 q 2),

Caetano [C] , Barthe [Bar ] ( 0 q 1).